1 Load packages and functions

1.1 Packages

library(ape)
library(phangorn)
library(caper)
library(tidyverse)
library(ggtree)
library(picante)
library(brms)
library(phangorn)
library(phytools)
library(treeio)
library(MASS)
library(car)
library(corrplot)
library(emmeans)
library(broom)
library(ggdist)
library(tidybayes)
library(raster)
library(sf)
library(exactextractr)
library(performance)

1.2 Functions

##Check ultrametric and/or fix
check_and_fix_ultrametric <- function(phy){
  
  if (!is.ultrametric(phy)){
    
    vv <- vcv.phylo(phy)
    dx <- diag(vv)
    mxx <- max(dx) - dx
    for (i in 1:length(mxx)){
      phy$edge.length[phy$edge[,2] == i] <- phy$edge.length[phy$edge[,2] == i] + mxx[i]
    }
    if (!is.ultrametric(phy)){
      stop("Ultrametric fix failed\n")
    }   
  }
  
  return(phy)
}
##Removed duplicated tips
remove_duplicate_tips<-function(tree){
for(spe in unique(tree$tip.label)){
  pos<-grep(paste("\\b",spe,"\\b",sep=""),tree$tip.label)
  if(length(pos)>1){
    rem<-pos[2:length(pos)]
    tree<-ape::drop.tip(phy=tree,tip=rem)
  } 
}
return(tree)
}

## Function for renaming tips
rename.tips.phylo <- function(tree, names) {
    tree$tip.label <- names
    return(tree)
}

#Stardarize variables

standard_varibles<-function(frame_data){
  for(nom in names(frame_data)){
    frame_data<-data.frame(frame_data)
    if(class(frame_data[,nom])!="numeric"){next}
    frame_data[,nom]<-scale(frame_data[,nom])[,1]
  }
  return(frame_data)
}

#standarize single variables

scale_single <- function(x){
  (x - mean(x, na.rm=TRUE)) / sd(x, na.rm=TRUE)
}

#Standard error function
se <- function(x) sd(x)/sqrt(length(x))

#Mean function 

meanfun <- function(data, i){
  d <- data[i, ]
  return(mean(d))   
}

#Variation coefficient

var_coef <- function(x, na.rm = FALSE) {
  sd(x, na.rm=na.rm) / mean(x, na.rm=na.rm)
}

2 Phylogeny setting

We are going to load the phylogenies of the two main families (Araneidae and Theridiidae) obtained in BEAST to removed duplicated tips and prune some outgroups to generate a single phylogeny for further analyses.

2.1 Araneidae phylogeny

#Load Araneidae tree
mcc_tree<-read.nexus("araneidae_new_final.tre")
#load fixed tip names
nam_tree<-read_csv("tip_names_araneidae.csv",col_names=T)
mcc_tree$tip.label<-nam_tree$corrected_name
###Remove repeated tips
tree_removedTips<-remove_duplicate_tips(mcc_tree)
##Remove tips to mix with Theridiidae tree
core<-extract.clade(phy=tree_removedTips,node=c(194), collapse.singles = TRUE,interactive = FALSE)
outgroups<- tree_removedTips$tip.label[which(tree_removedTips$tip.label %in% core$tip.label==FALSE)]
outgroups_araneidae<-outgroups
tree_removedTips<-drop.tip(tree_removedTips,outgroups)

2.2 Theridiidae phylogeny

#Load Theridiidae tree
tree_theridiidae<-read.nexus("total_Theridiidae_tree.tre")
#load fixed tip names
nam_tree<-read_delim("theridiidae_tips.txt",col_names=F)
tree_theridiidae$tip.label<-nam_tree$X2
#Remove repeated tips
tree_removed_theridiidae<-remove_duplicate_tips(tree_theridiidae)
#remove problematic tips
problematic_tips<-c("Chrysso_albipes","Chrysso_sp","Erigone_dentosa")
tree_removed_theridiidae<-drop.tip(tree_removed_theridiidae,c(problematic_tips))
#Identify the outgroup
#plotTree(tree_removed_theridiidae) 
#nodelabels()
outgroups<-extract.clade(phy=tree_removed_theridiidae, node=304, root.edge = 0, collapse.singles = TRUE,interactive = FALSE) #Keep an eye on the node
outgroups_theridiidae<-outgroups

Now with the two phylogenies, we are going to join them fro further analyses

2.3 Join the phylogenies

calib<-makeChronosCalib(tree_removed_theridiidae, age.min = max(node.depth.edgelength(tree_removedTips)), age.max = max(node.depth.edgelength(tree_removedTips)))
tmp_t<-chronos(tree_removed_theridiidae, lambda = 1, model = "correlated", quiet = FALSE,
        calibration = calib,
        control = chronos.control())
## 
## Setting initial dates...
## Fitting in progress... get a first set of estimates
##          (Penalised) log-lik = -628.3153 
## Optimising rates... dates... -628.3153 
## 
## log-Lik = -628.3153 
## PHIIC = 2190.63
joint_trees_outgroups<-bind.tree(tree_removedTips,tmp_t, interactive = FALSE)
joint_trees<-bind.tree(tree_removedTips, ape::drop.tip(phy=tmp_t,outgroups$tip.label), interactive = FALSE)

# get scaled edge.length
joint_trees$edge.length <- joint_trees$edge.length / (max(joint_trees$edge.length))

#Remove duplicate tips
joint_trees<-remove_duplicate_tips(joint_trees)
#Check that the final tree is ultrametric
joint_trees<-check_and_fix_ultrametric(joint_trees)

3 Load data and data matching

#load the csv file
join_dataset<-read_csv("data_total.csv",col_names=T)
#replace spaces in species names
join_dataset$species<-gsub(pattern=" ", replacement="_",join_dataset$species)
#keep unique rows
join_dataset<-distinct(join_dataset,species,.keep_all = TRUE)
#Tranform presence in islands to a binary variable
join_dataset<-join_dataset %>% mutate(bin_island=ifelse(cat_island=="island"|cat_island=="island_continent",1,0))
#replace spaces in species names on the tree
join_tree<-multi2di(joint_trees)
join_tree$tip.label<-gsub(pattern=" ", replacement="_",join_tree$tip.label)
##Check if the table match the tree tips
#remove species that are not in the phylogeny
join_dataset<-join_dataset[join_dataset$species %in% join_tree$tip.label,]
##Add species with no information into the phylogeny, like XX_sp
for(spe in unique(join_tree$tip.label)){
  #Remove 
  if(spe %in% join_dataset$species==FALSE){
    print(spe)
    join_dataset<-join_dataset %>% add_row(species=spe)
  } 
}

#Let's modify the dataset to deal with colour polytipic species
join_dataset$polymorphism[which(join_dataset$polymorphism %in% c("polytipic","possible polytipic","pattern variable")==TRUE)]<-NA
join_dataset<-join_dataset %>% filter(!is.na(polymorphism))

dataset_all_species_phylogeny<-join_dataset

Now we have a single and a dataset that match each other.

4 Phylogeny visualization

Let’s see how is the presence of colour polymorphism present in the phylogeny

#Change tree name
to_plot_tree<-join_tree
#Find colour polymorphic lineages
otus<-join_dataset %>% filter(polymorphism=="yes") %>% pull(species)
to_plot_tree<-groupOTU(to_plot_tree, otus)
df_polymorphism<-data.frame(join_dataset$polymorphism)
#df_island<-data.frame(as.character(join_dataset$bin_island))
rownames(df_polymorphism)<-join_dataset$species
#Plot tree with names
p<-ggtree(to_plot_tree, layout='circular') + geom_tiplab()
#pdf("total_tree_names.pdf", width=20,height=20)
#plot(p)
#dev.off()
#Plot tree colour polymorphism
p<-ggtree(to_plot_tree, layout='circular')
#pdf("total_tree_polymorphism.pdf", width=20,height=20)
gheatmap(p, df_polymorphism, offset=.001, width=.08,colnames = FALSE, colnames_offset_y = 1)+scale_fill_manual(values=c("#1ABEC6","#FF5B00"),name="Presence of\ncolour polymorphism")

#dev.off()

5 Filter species with poor geographical information

Arachnids is one of the groups with the poorest geographic information available in public databases.For instance, in our data ~51% of the species has less than 50 geographical records

species_points<-join_dataset %>% drop_na(n_points)
species_geo<-nrow(species_points[species_points$n_points<50,])/nrow(species_points)*100
print(paste0(species_geo,"%"," of the species with geographical information has less than 50 geographical records"))
## [1] "52.6881720430108% of the species with geographical information has less than 50 geographical records"

To account for this, we decided to calculated the mean and its 95% confidence interval (CI) for the number of geographical records available for all the species. We excluded species from the subsequent analyses that fell outside the lower CI.

#Due to high vari
l_points<-na.omit(log(join_dataset$n_points))
##Let's calculate the 95% around the mean
library(boot)
data <- data.frame(xs = l_points)
bo <- boot(data[, "xs", drop = FALSE], statistic=meanfun, R=5000)
mean_ci<-boot.ci(bo, conf=0.95, type="bca")

ggplot(tibble(x=bo$t[,1]), aes(x=x)) +geom_density()+geom_segment(x=mean_ci$bca[4],xend=mean_ci$bca[5],y=0,yend=0,color="blue",size=2,lineend="round")

##Remove species with low number of records
datos_filtered<-join_dataset %>% filter(n_points>=exp(mean_ci$bca[4]))

#let's keep this filtered dataset for further analyses

data_filtered_phylogeny<-datos_filtered

6 Statistical models with the remaining species

all the predictors seems skewed or not uniform distributed, let’s modify some predictors that may affect the regression due to their non-normal distribution

datos_filtered$T_centroid_lat<-abs(datos_filtered$centroid_lat)   
datos_filtered$T_lat_range<-sqrt(abs(datos_filtered$lat_range))
datos_filtered$T_area_polygon<-sqrt(datos_filtered$area_polygon+1)
datos_filtered$T_lat_range_wsc<-abs(datos_filtered$lat_range_wsc)
datos_filtered$T_area_countries_wsc<-sqrt(datos_filtered$area_countries_wsc)
datos_filtered$T_points<-log(datos_filtered$n_points)
datos_filtered$T_bole<-log(datos_filtered$bole_female)

6.1 Analyses total samples

Remove species from islands that can affect calculations due to their geographic limit for dispersion

datos_filtered_total<-datos_filtered %>% filter(cat_island != "island") %>% data.frame()

Number of colour monomorphic and polymorphic species

table(datos_filtered_total$polymorphism)
## 
##  no yes 
##  55  33

Correlation plot between the variables

cor_matrix <- cor(na.omit(datos_filtered_total[,c("T_points","T_centroid_lat","T_bole","T_lat_range","T_area_polygon","eco_reg_points","eco_reg_polygon","temp_zones_points","temp_zones_polygon")]))

colnames(cor_matrix)<c("T_points","T_centroid_lat","T_bole","T_lat_range","T_area_polygon","eco_reg_points","eco_reg_polygon","temp_zones_points","temp_zones_polygon")
## [1] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
rownames(cor_matrix)<-c("T_points","T_centroid_lat","T_bole","T_lat_range","T_area_polygon","eco_reg_points","eco_reg_polygon","temp_zones_points","temp_zones_polygon")
par(mfrow=c(1,1))
corrplot(cor_matrix, method = "number", type = "upper", order = "original", tl.cex=1, )

Standardize variable before the analysis, excluding the count variables

datos_filtered_total[,c("T_points","T_centroid_lat","T_bole","T_lat_range","T_area_polygon")]<-standard_varibles(datos_filtered_total[,c("T_points","T_centroid_lat","T_bole","T_lat_range","T_area_polygon")]) %>% data.frame()

Now, let’s prepare the dataset and tree so they match, this is super important. Your phylogeny names need to match a column of data

Let’s run the models!

6.1.1 Association between colour polymorphism and number of records and latitude of the centroid

Evaluate if the colour monomorphic and colour polymorphic species differ in the number of records

set.seed(30011994)
brm_points <- brm(
 n_points ~ polymorphism+(1| gr(species, cov = A)) ,
  data = datos_filtered_total,
  family = poisson(),
  #prior = prior,
  data2 = list(A = A),
  control = list(adapt_delta = 0.999, max_treedepth=10)
  ,chains = 4, cores = 4, iter = 20000
)
## Compiling Stan program...
## Start sampling
## Warning: There were 40000 transitions after warmup that exceeded the maximum treedepth. Increase max_treedepth above 10. See
## https://mc-stan.org/misc/warnings.html#maximum-treedepth-exceeded
## Warning: Examine the pairs() plot to diagnose sampling problems
## Warning: The largest R-hat is 1.06, indicating chains have not mixed.
## Running the chains for more iterations may help. See
## https://mc-stan.org/misc/warnings.html#r-hat
## Warning: Bulk Effective Samples Size (ESS) is too low, indicating posterior means and medians may be unreliable.
## Running the chains for more iterations may help. See
## https://mc-stan.org/misc/warnings.html#bulk-ess
## Warning: Tail Effective Samples Size (ESS) is too low, indicating posterior variances and tail quantiles may be unreliable.
## Running the chains for more iterations may help. See
## https://mc-stan.org/misc/warnings.html#tail-ess
#pairs(brm_points)
summary(brm_points)
## Warning: Parts of the model have not converged (some Rhats are > 1.05). Be
## careful when analysing the results! We recommend running more iterations and/or
## setting stronger priors.
##  Family: poisson 
##   Links: mu = log 
## Formula: n_points ~ polymorphism + (1 | gr(species, cov = A)) 
##    Data: datos_filtered_total (Number of observations: 88) 
##   Draws: 4 chains, each with iter = 20000; warmup = 10000; thin = 1;
##          total post-warmup draws = 40000
## 
## Group-Level Effects: 
## ~species (Number of levels: 88) 
##               Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept)     2.92      0.21     2.53     3.36 1.03      113      310
## 
## Population-Level Effects: 
##                 Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept           6.01      0.92     4.26     7.78 1.05       60      109
## polymorphismyes     0.88      0.48    -0.11     1.80 1.05       60      141
## 
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).
## Check if the predicted values fits the rawdata
#r2
r2_bayes(brm_points)
## # Bayesian R2 with Compatibility Interval
## 
##   Conditional R2: 1.000 (95% CI [1.000, 1.000])
##      Marginal R2: 0.014 (95% CI [4.560e-11, 0.269])
#
pp_check(brm_points)
## Using 10 posterior draws for ppc type 'dens_overlay' by default.

##Preliminary plots
plot(conditional_effects(brm_points))

They do not have differences in the number of records

Evaluate if the colour monomorphic and colour polymorphic species differ in the latitude of the centroid

set.seed(30011994)
brm_centroid <- brm(
  T_centroid_lat ~ polymorphism+(1| gr(species, cov = A)) ,
  data = datos_filtered_total,
  family = skew_normal(),
  #prior = prior,
  data2 = list(A = A),
  control = list(adapt_delta = 0.999, max_treedepth=10)
  ,chains = 4, cores = 4, iter = 1000
)
## Compiling Stan program...
## Start sampling
## Warning: There were 3 chains where the estimated Bayesian Fraction of Missing Information was low. See
## https://mc-stan.org/misc/warnings.html#bfmi-low
## Warning: Examine the pairs() plot to diagnose sampling problems
## Warning: Bulk Effective Samples Size (ESS) is too low, indicating posterior means and medians may be unreliable.
## Running the chains for more iterations may help. See
## https://mc-stan.org/misc/warnings.html#bulk-ess
## Warning: Tail Effective Samples Size (ESS) is too low, indicating posterior variances and tail quantiles may be unreliable.
## Running the chains for more iterations may help. See
## https://mc-stan.org/misc/warnings.html#tail-ess
pairs(brm_centroid)

summary(brm_centroid)
##  Family: skew_normal 
##   Links: mu = identity; sigma = identity; alpha = identity 
## Formula: T_centroid_lat ~ polymorphism + (1 | gr(species, cov = A)) 
##    Data: datos_filtered_total (Number of observations: 88) 
##   Draws: 4 chains, each with iter = 1000; warmup = 500; thin = 1;
##          total post-warmup draws = 2000
## 
## Group-Level Effects: 
## ~species (Number of levels: 88) 
##               Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept)     0.88      0.18     0.56     1.26 1.02      114      209
## 
## Population-Level Effects: 
##                 Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept          -0.04      0.31    -0.68     0.50 1.01      488      411
## polymorphismyes    -0.13      0.21    -0.53     0.27 1.00     1052     1344
## 
## Family Specific Parameters: 
##       Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma     0.56      0.14     0.27     0.82 1.02      106      138
## alpha    -3.80      2.82    -9.56     1.77 1.00      548      621
## 
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).
#r2
r2_bayes(brm_centroid)
## # Bayesian R2 with Compatibility Interval
## 
##   Conditional R2: 0.674 (95% CI [0.425, 0.953])
##      Marginal R2: 0.007 (95% CI [2.683e-09, 0.051])
## Check if the predicted values fits the rawdata
pp_check(brm_centroid)
## Using 10 posterior draws for ppc type 'dens_overlay' by default.

##Preliminary plots
plot(conditional_effects(brm_centroid))

They do not have differences in the latitude of the centroid

Evaluate if the colour monomorphic and colour polymorphic species differ in the body length

set.seed(30011994)
brm_bole <- brm(
  T_bole ~ polymorphism+(1| gr(species, cov = A)) ,
  data = datos_filtered_total,
  family = gaussian(),
  #prior = prior,
  data2 = list(A = A),
  control = list(adapt_delta = 0.999, max_treedepth=10)
  ,chains = 4, cores = 4, iter = 20000
)
## Warning: Rows containing NAs were excluded from the model.
## Compiling Stan program...
## Start sampling
## Warning: There were 16 divergent transitions after warmup. See
## https://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup
## to find out why this is a problem and how to eliminate them.
## Warning: There were 384 transitions after warmup that exceeded the maximum treedepth. Increase max_treedepth above 10. See
## https://mc-stan.org/misc/warnings.html#maximum-treedepth-exceeded
## Warning: There were 4 chains where the estimated Bayesian Fraction of Missing Information was low. See
## https://mc-stan.org/misc/warnings.html#bfmi-low
## Warning: Examine the pairs() plot to diagnose sampling problems
## Warning: Bulk Effective Samples Size (ESS) is too low, indicating posterior means and medians may be unreliable.
## Running the chains for more iterations may help. See
## https://mc-stan.org/misc/warnings.html#bulk-ess
## Warning: Tail Effective Samples Size (ESS) is too low, indicating posterior variances and tail quantiles may be unreliable.
## Running the chains for more iterations may help. See
## https://mc-stan.org/misc/warnings.html#tail-ess
pairs(brm_bole)

summary(brm_bole)
## Warning: There were 16 divergent transitions after warmup. Increasing
## adapt_delta above 0.999 may help. See
## http://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup
##  Family: gaussian 
##   Links: mu = identity; sigma = identity 
## Formula: T_bole ~ polymorphism + (1 | gr(species, cov = A)) 
##    Data: datos_filtered_total (Number of observations: 87) 
##   Draws: 4 chains, each with iter = 20000; warmup = 10000; thin = 1;
##          total post-warmup draws = 40000
## 
## Group-Level Effects: 
## ~species (Number of levels: 87) 
##               Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept)     0.99      0.11     0.78     1.20 1.00     1369     3447
## 
## Population-Level Effects: 
##                 Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept           0.03      0.32    -0.61     0.66 1.00     3377     4174
## polymorphismyes    -0.09      0.18    -0.44     0.26 1.00     4315    10220
## 
## Family Specific Parameters: 
##       Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma     0.24      0.11     0.05     0.47 1.01      315      153
## 
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).
## Check if the predicted values fits the rawdata
#r2
r2_bayes(brm_bole)
## # Bayesian R2 with Compatibility Interval
## 
##   Conditional R2: 0.947 (95% CI [0.823, 1.000])
##      Marginal R2: 0.004 (95% CI [1.427e-12, 0.032])
pp_check(brm_bole)
## Using 10 posterior draws for ppc type 'dens_overlay' by default.

##Preliminary plots
plot(conditional_effects(brm_bole))

They do not have differences in body length

let’s Evaluate the association fo the predictors

lm_lat_range <- lm(T_lat_range ~ polymorphism+T_bole+T_centroid_lat, data=datos_filtered_total)

check_collinearity(lm_lat_range)

The predictors are not collinear, we can use all of them in the models

6.1.2 Latitudinal range

set.seed(30011994)
brm_latrange_1 <- brm(
 T_lat_range ~ polymorphism+T_bole+T_centroid_lat + (1| gr(species, cov = A)) ,
  data = datos_filtered_total,
  family = gaussian(),
  #prior = prior,
  data2 = list(A = A),
  control = list(adapt_delta = 0.999, max_treedepth=10)
  ,chains = 4, cores = 4, iter = 20000
)
## Warning: Rows containing NAs were excluded from the model.
## Compiling Stan program...
## Start sampling
pairs(brm_latrange_1)

summary(brm_latrange_1)
##  Family: gaussian 
##   Links: mu = identity; sigma = identity 
## Formula: T_lat_range ~ polymorphism + T_bole + T_centroid_lat + (1 | gr(species, cov = A)) 
##    Data: datos_filtered_total (Number of observations: 87) 
##   Draws: 4 chains, each with iter = 20000; warmup = 10000; thin = 1;
##          total post-warmup draws = 40000
## 
## Group-Level Effects: 
## ~species (Number of levels: 87) 
##               Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept)     0.47      0.29     0.03     1.09 1.00     2027     2770
## 
## Population-Level Effects: 
##                 Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept          -0.13      0.22    -0.56     0.31 1.00    17954    14689
## polymorphismyes     0.46      0.23     0.02     0.91 1.00    15162    23355
## T_bole              0.14      0.13    -0.10     0.39 1.00    27163    24394
## T_centroid_lat     -0.38      0.12    -0.61    -0.14 1.00    25869    29033
## 
## Family Specific Parameters: 
##       Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma     0.81      0.13     0.50     1.02 1.00     2455     2539
## 
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).
## Check if the predicted values fits the rawdata
#r2
r2_bayes(brm_latrange_1)
## # Bayesian R2 with Compatibility Interval
## 
##   Conditional R2: 0.368 (95% CI [0.134, 0.719])
##      Marginal R2: 0.281 (95% CI [0.126, 0.423])
pp_check(brm_latrange_1)
## Using 10 posterior draws for ppc type 'dens_overlay' by default.

##Preliminary plots
plot(conditional_effects(brm_latrange_1))

6.1.3 Range size calculated with the area of the Convex polygon

area_polygon_1 <- brm(
 T_area_polygon ~ polymorphism+T_bole+T_centroid_lat + (1| gr(species, cov = A)),
  data = datos_filtered_total,
  family = skew_normal(),
  #prior = prior,
  data2 = list(A = A),
  control = list(adapt_delta = 0.999, max_treedepth=10)
  ,chains = 4, cores = 4, iter = 20000
)
## Warning: Rows containing NAs were excluded from the model.
## Compiling Stan program...
## Start sampling
pairs(area_polygon_1)

summary(area_polygon_1)
##  Family: skew_normal 
##   Links: mu = identity; sigma = identity; alpha = identity 
## Formula: T_area_polygon ~ polymorphism + T_bole + T_centroid_lat + (1 | gr(species, cov = A)) 
##    Data: datos_filtered_total (Number of observations: 86) 
##   Draws: 4 chains, each with iter = 20000; warmup = 10000; thin = 1;
##          total post-warmup draws = 40000
## 
## Group-Level Effects: 
## ~species (Number of levels: 86) 
##               Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept)     0.25      0.17     0.01     0.62 1.00     9849    15045
## 
## Population-Level Effects: 
##                 Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept          -0.05      0.17    -0.38     0.30 1.00    47271    29072
## polymorphismyes     0.30      0.21    -0.11     0.72 1.00    52964    31354
## T_bole              0.12      0.12    -0.11     0.36 1.00    50018    30576
## T_centroid_lat      0.12      0.13    -0.12     0.37 1.00    55075    30681
## 
## Family Specific Parameters: 
##       Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma     0.96      0.09     0.80     1.15 1.00    30978    24118
## alpha     3.56      1.54     1.35     7.45 1.00    24221    18226
## 
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).
## Check if the predicted values fits the rawdata
#r2
r2_bayes(area_polygon_1)
## # Bayesian R2 with Compatibility Interval
## 
##   Conditional R2: 0.103 (95% CI [0.005, 0.253])
##      Marginal R2: 0.060 (95% CI [0.001, 0.154])
pp_check(area_polygon_1)
## Using 10 posterior draws for ppc type 'dens_overlay' by default.

##Preliminary plots
plot(conditional_effects(area_polygon_1))

6.1.4 Ecological regions

To indirectly explore the difference in niche width between colour monomorphic and polymorphic species, we measured the number of ecological regions occupy by each species using the geographical records and polygons. the ecological regions were obtained here

BRMS model exploring differences in the ecological regions occupy by monomorphic and polymorphic species based on geographical records

set.seed(30011994)
eco_reg_points_1 <- brm(
 eco_reg_points ~  polymorphism+T_bole+T_centroid_lat + (1| gr(species, cov = A)) ,
  data = datos_filtered_total,
  family = poisson(),
  #prior = prior,
  data2 = list(A = A),
  control = list(adapt_delta = 0.999, max_treedepth=20)
  ,chains = 4, cores = 4, iter = 20000
)
## Warning: Rows containing NAs were excluded from the model.
## Compiling Stan program...
## Start sampling
pairs(eco_reg_points_1)

summary(eco_reg_points_1)
##  Family: poisson 
##   Links: mu = log 
## Formula: eco_reg_points ~ polymorphism + T_bole + T_centroid_lat + (1 | gr(species, cov = A)) 
##    Data: datos_filtered_total (Number of observations: 87) 
##   Draws: 4 chains, each with iter = 20000; warmup = 10000; thin = 1;
##          total post-warmup draws = 40000
## 
## Group-Level Effects: 
## ~species (Number of levels: 87) 
##               Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept)     1.25      0.12     1.04     1.50 1.00     8809    15355
## 
## Population-Level Effects: 
##                 Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept           3.09      0.40     2.31     3.86 1.00     5945    11406
## polymorphismyes     0.41      0.21    -0.00     0.83 1.00     6282    12313
## T_bole              0.27      0.14    -0.01     0.55 1.00     7752    13787
## T_centroid_lat      0.12      0.12    -0.11     0.35 1.00     6849    13123
## 
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).
## Check if the predicted values fits the rawdata
#r2
r2_bayes(eco_reg_points_1)
## # Bayesian R2 with Compatibility Interval
## 
##   Conditional R2: 0.964 (95% CI [0.947, 0.977])
##      Marginal R2: 0.112 (95% CI [1.779e-04, 0.387])
pp_check(eco_reg_points_1)
## Using 10 posterior draws for ppc type 'dens_overlay' by default.

##Preliminary plots
plot(conditional_effects(eco_reg_points_1))

BRMS model exploring differences in the ecological regions occupy by monomorphic and polymorphic species based on polygon

eco_reg_polygon_1 <- brm(
 eco_reg_polygon~ polymorphism+T_bole+T_centroid_lat + (1| gr(species, cov = A)) ,
  data = datos_filtered_total,
  family = poisson(),
  #prior = prior,
  data2 = list(A = A),
  control = list(adapt_delta = 0.999, max_treedepth=20)
  ,chains = 4, cores = 4, iter = 20000
)
## Warning: Rows containing NAs were excluded from the model.
## Compiling Stan program...
## Start sampling
pairs(eco_reg_polygon_1)

summary(eco_reg_polygon_1)
##  Family: poisson 
##   Links: mu = log 
## Formula: eco_reg_polygon ~ polymorphism + T_bole + T_centroid_lat + (1 | gr(species, cov = A)) 
##    Data: datos_filtered_total (Number of observations: 86) 
##   Draws: 4 chains, each with iter = 20000; warmup = 10000; thin = 1;
##          total post-warmup draws = 40000
## 
## Group-Level Effects: 
## ~species (Number of levels: 86) 
##               Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept)     1.34      0.12     1.13     1.59 1.00     6283    11297
## 
## Population-Level Effects: 
##                 Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept           3.73      0.43     2.91     4.57 1.00     4766     8879
## polymorphismyes     0.43      0.23    -0.01     0.88 1.00     4972     8896
## T_bole              0.34      0.15     0.04     0.63 1.00     5044     9268
## T_centroid_lat     -0.20      0.12    -0.45     0.04 1.00     5055     8872
## 
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).
#r2
r2_bayes(eco_reg_polygon_1)
## # Bayesian R2 with Compatibility Interval
## 
##   Conditional R2: 0.985 (95% CI [0.978, 0.991])
##      Marginal R2: 0.212 (95% CI [0.013, 0.505])
## Check if the predicted values fits the rawdata
pp_check(eco_reg_polygon_1)
## Using 10 posterior draws for ppc type 'dens_overlay' by default.

##Preliminary plots
plot(conditional_effects(eco_reg_polygon_1))

6.1.5 Climatic zones

Addtionally, we also explored if colour monomorphic and polymorphic species differ in the number of climatic zones they occupy. We measured the number of climatic zones for each species using the geographical records and polygons. the Köppen-Geiger climate classification zones were obtained here

temp_zones_points_1 <- brm(
 temp_zones_points~ polymorphism+T_bole+T_centroid_lat + (1| gr(species, cov = A)) ,
  data = datos_filtered_total,
  family = negbinomial(),
  #prior = prior,
  data2 = list(A = A),
  control = list(adapt_delta = 0.999, max_treedepth=20)
  ,chains = 4, cores = 4, iter = 20000
)
## Warning: Rows containing NAs were excluded from the model.
## Compiling Stan program...
## Start sampling
pairs(temp_zones_points_1)

summary(temp_zones_points_1)
##  Family: negbinomial 
##   Links: mu = log; shape = identity 
## Formula: temp_zones_points ~ polymorphism + T_bole + T_centroid_lat + (1 | gr(species, cov = A)) 
##    Data: datos_filtered_total (Number of observations: 87) 
##   Draws: 4 chains, each with iter = 20000; warmup = 10000; thin = 1;
##          total post-warmup draws = 40000
## 
## Group-Level Effects: 
## ~species (Number of levels: 87) 
##               Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept)     0.11      0.08     0.00     0.29 1.00     9680    17461
## 
## Population-Level Effects: 
##                 Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept           2.04      0.07     1.88     2.18 1.00    34189    23133
## polymorphismyes     0.16      0.09    -0.02     0.34 1.00    50666    28279
## T_bole              0.19      0.05     0.09     0.29 1.00    47745    30749
## T_centroid_lat      0.09      0.05    -0.00     0.19 1.00    50836    31777
## 
## Family Specific Parameters: 
##       Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## shape    56.56     52.85    12.46   202.97 1.00    40605    31129
## 
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).
#r2
r2_bayes(temp_zones_points_1)
## # Bayesian R2 with Compatibility Interval
## 
##   Conditional R2: 0.267 (95% CI [0.108, 0.450])
##      Marginal R2: 0.225 (95% CI [0.072, 0.385])
## Check if the predicted values fits the rawdata
pp_check(temp_zones_points_1)
## Using 10 posterior draws for ppc type 'dens_overlay' by default.

##Preliminary plots
plot(conditional_effects(temp_zones_points_1))

temp_zones_polygon_1 <- brm(
 temp_zones_polygon~polymorphism+T_bole+T_centroid_lat+ (1| gr(species, cov = A)) ,
  data = datos_filtered_total,
  family = negbinomial(),
  #prior = prior,
  data2 = list(A = A),
  control = list(adapt_delta = 0.999, max_treedepth=20)
  ,chains = 4, cores = 4, iter = 20000
)
## Warning: Rows containing NAs were excluded from the model.
## Compiling Stan program...
## Start sampling
pairs(temp_zones_polygon_1)

summary(temp_zones_polygon_1)
##  Family: negbinomial 
##   Links: mu = log; shape = identity 
## Formula: temp_zones_polygon ~ polymorphism + T_bole + T_centroid_lat + (1 | gr(species, cov = A)) 
##    Data: datos_filtered_total (Number of observations: 86) 
##   Draws: 4 chains, each with iter = 20000; warmup = 10000; thin = 1;
##          total post-warmup draws = 40000
## 
## Group-Level Effects: 
## ~species (Number of levels: 86) 
##               Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept)     0.08      0.07     0.00     0.25 1.00    13062    16673
## 
## Population-Level Effects: 
##                 Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept           2.55      0.07     2.40     2.69 1.00    34319    25230
## polymorphismyes     0.00      0.10    -0.20     0.20 1.00    45404    29705
## T_bole              0.03      0.06    -0.09     0.13 1.00    36527    29929
## T_centroid_lat     -0.18      0.06    -0.29    -0.07 1.00    38854    30488
## 
## Family Specific Parameters: 
##       Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## shape     9.48      3.40     5.15    17.34 1.00    37365    22585
## 
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).
#r2
r2_bayes(temp_zones_polygon_1)
## # Bayesian R2 with Compatibility Interval
## 
##   Conditional R2: 0.243 (95% CI [0.090, 0.395])
##      Marginal R2: 0.206 (95% CI [0.059, 0.357])
## Check if the predicted values fits the rawdata
pp_check(temp_zones_polygon_1)
## Using 10 posterior draws for ppc type 'dens_overlay' by default.

##Preliminary plots
plot(conditional_effects(temp_zones_polygon_1))

all_models<-NULL

for(mod in c("brm_latrange_1","area_polygon_1","eco_reg_points_1","eco_reg_polygon_1","temp_zones_polygon_1","temp_zones_points_1")){
baye_mode = get(mod)
  bayes_results<-baye_mode %>% 
  spread_draws(b_polymorphismyes)
  bayes_results<-tibble(b_polymorphismyes=bayes_results$b_polymorphismyes,model=mod)
  all_models<-bind_rows(all_models, bayes_results)
} 

all_models %>% ggplot(aes(y = model, x = b_polymorphismyes)) +
  stat_halfeye()+
  theme_classic()+
  geom_vline(xintercept = 0, linetype = "dashed",col="black",size=1)+
  labs(x="Estimate",y="Models")

Plot of the model

paleta1<-c("#1ABEC6","#FF5B00")

dataset_plot<-datos_filtered_total %>% drop_na(T_lat_range|polymorphism|T_bole|T_centroid_lat)

dataset_plot$predict<-predict(brm_latrange_1,type="response")[,"Estimate"]

dataset_plot %>% ggplot(aes(x=polymorphism,y=predict,fill=polymorphism))+geom_point(aes(x=polymorphism,y=T_lat_range),shape = 21,size=3, position = position_jitterdodge(),alpha=0.5)+geom_violin(aes(x=polymorphism,y=T_lat_range),alpha=0.1, position = position_dodge(width = .75),size=1)+
  stat_summary(fun = mean,aes(color = polymorphism,group=polymorphism),fun.min = function(x) mean(x) - (2*se(x)),fun.max = function(x) mean(x)+(2*se(x)),geom = "pointrange",shape=22,size=1.5,col="black")+scale_fill_manual(values=paleta1)+scale_colour_manual(values=paleta1)+theme_classic()+labs(x="Colour polymorphism",y="Latitudinal range")

6.2 Predictive confidence interval

To eliminate any false association caused by sampling bias, we repeated the above analyses with a reduced dataset. The subset was created by calculating a linear regression between the number of geographical records and the geographical area of the regions described in the WSC (a positive relationship), and then discarding species outside the lower boundary of the 50% predictive confidence interval (Quantile 0.75 and Quantile 0.25). In this way we only kept species with a small number of records when their WSC calculated range was calculated as very small (Predictive interval subset; supplementary figure 2). This approach is different from using a threshold for the number of points because it acknowledges that some species will have fewer records if their range is very restricted.

Let’s generate the dataset

no_island<-datos_filtered %>% filter(cat_island!="island") %>% drop_na(n_points) %>% drop_na(area_polygon) %>%drop_na(polymorphism)

no_island<-na.omit(no_island)

no_island[,c("T_points","T_centroid_lat","T_bole","T_lat_range","T_area_polygon")]<-standard_varibles(no_island[,c("T_points","T_centroid_lat","T_bole","T_lat_range","T_area_polygon")]) %>% data.frame()

lm_points<-lm(T_points~T_area_countries_wsc,data=no_island)
summary(lm_points)
## 
## Call:
## lm(formula = T_points ~ T_area_countries_wsc, data = no_island)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -2.3549 -0.5525 -0.0333  0.5903  1.7387 
## 
## Coefficients:
##                        Estimate Std. Error t value Pr(>|t|)    
## (Intercept)          -1.694e+00  3.466e-01  -4.889 5.73e-06 ***
## T_area_countries_wsc  3.289e-04  6.445e-05   5.103 2.50e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8659 on 74 degrees of freedom
## Multiple R-squared:  0.2603, Adjusted R-squared:  0.2503 
## F-statistic: 26.04 on 1 and 74 DF,  p-value: 2.503e-06
no_island<-cbind(no_island,predict(lm_points,interval="prediction",level=0.50))## this plots the q10% and q90%
## Warning in predict.lm(lm_points, interval = "prediction", level = 0.5): predictions on current data refer to _future_ responses
ggplot(no_island,aes(T_area_countries_wsc,T_points))+geom_point(size=3,aes(col=polymorphism))+ geom_smooth(method = "lm",level=0.99)+geom_line(aes(y=upr),col="red")+geom_line(aes(y=lwr),col="red")+theme_bw()
## `geom_smooth()` using formula = 'y ~ x'

##subset based on the prediction intervals
pi_subset<-no_island[!no_island$T_points<no_island$lwr,]

Number of colour monomorphic and polymorphic species after filtering

table(pi_subset$polymorphism)
## 
##  no yes 
##  35  24

Correlation plot between the variables

cor_matrix <- cor(na.omit(pi_subset[,c("T_points","T_centroid_lat","T_bole","T_lat_range","T_area_polygon","eco_reg_points","eco_reg_polygon","temp_zones_points","temp_zones_polygon")]))

colnames(cor_matrix)<c("T_points","T_centroid_lat","T_bole","T_lat_range","T_area_polygon","eco_reg_points","eco_reg_polygon","temp_zones_points","temp_zones_polygon")
## [1] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
rownames(cor_matrix)<-c("T_points","T_centroid_lat","T_bole","T_lat_range","T_area_polygon","eco_reg_points","eco_reg_polygon","temp_zones_points","temp_zones_polygon")
par(mfrow=c(1,1))
corrplot(cor_matrix, method = "number", type = "upper", order = "original", tl.cex=1, )

Standardize variable before the analysis, excluding the count variables

pi_subset[,c("T_points","T_centroid_lat","T_bole","T_lat_range","T_area_polygon")]<-standard_varibles(pi_subset[,c("T_points","T_centroid_lat","T_bole","T_lat_range","T_area_polygon")]) %>% data.frame()

Now, let’s prepare the dataset and tree so they match, this is super important. Your phylogeny names need to match a column of data

Let’s run the models!

6.2.1 Association between colour polymorphism and number of records and latitude of the centroid

Evaluate if the colour monomorphic and colour polymorphic species differ in the number of records

set.seed(30011994)
brm_points <- brm(
 n_points ~ polymorphism+(1| gr(species, cov = A)) ,
  data = pi_subset,
  family = poisson(),
  #prior = prior,
  data2 = list(A = A),
  control = list(adapt_delta = 0.999, max_treedepth=10)
  ,chains = 4, cores = 4, iter = 20000
)
## Compiling Stan program...
## Start sampling
## Warning: There were 34494 transitions after warmup that exceeded the maximum treedepth. Increase max_treedepth above 10. See
## https://mc-stan.org/misc/warnings.html#maximum-treedepth-exceeded
## Warning: Examine the pairs() plot to diagnose sampling problems
## Warning: The largest R-hat is 1.06, indicating chains have not mixed.
## Running the chains for more iterations may help. See
## https://mc-stan.org/misc/warnings.html#r-hat
## Warning: Bulk Effective Samples Size (ESS) is too low, indicating posterior means and medians may be unreliable.
## Running the chains for more iterations may help. See
## https://mc-stan.org/misc/warnings.html#bulk-ess
## Warning: Tail Effective Samples Size (ESS) is too low, indicating posterior variances and tail quantiles may be unreliable.
## Running the chains for more iterations may help. See
## https://mc-stan.org/misc/warnings.html#tail-ess
pairs(brm_points)

summary(brm_points)
## Warning: Parts of the model have not converged (some Rhats are > 1.05). Be
## careful when analysing the results! We recommend running more iterations and/or
## setting stronger priors.
##  Family: poisson 
##   Links: mu = log 
## Formula: n_points ~ polymorphism + (1 | gr(species, cov = A)) 
##    Data: pi_subset (Number of observations: 59) 
##   Draws: 4 chains, each with iter = 20000; warmup = 10000; thin = 1;
##          total post-warmup draws = 40000
## 
## Group-Level Effects: 
## ~species (Number of levels: 59) 
##               Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept)     2.55      0.24     2.13     3.07 1.03      165      401
## 
## Population-Level Effects: 
##                 Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept           6.68      0.84     4.95     8.37 1.04       66      106
## polymorphismyes     0.93      0.54    -0.14     2.13 1.06       68      107
## 
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).
#r2
r2_bayes(brm_points)
## # Bayesian R2 with Compatibility Interval
## 
##   Conditional R2: 1.000 (95% CI [0.999, 1.000])
##      Marginal R2: 0.056 (95% CI [9.213e-11, 0.457])
## Check if the predicted values fits the rawdata
pp_check(brm_points)
## Using 10 posterior draws for ppc type 'dens_overlay' by default.

##Preliminary plots
plot(conditional_effects(brm_points))

They do not have differences in the number of records

Evaluate if the colour monomorphic and colour polymorphic species differ in the latitude of the centroid

set.seed(30011994)
brm_centroid <- brm(
  T_centroid_lat ~ polymorphism+(1| gr(species, cov = A)) ,
  data = pi_subset,
  family = skew_normal(),
  #prior = prior,
  data2 = list(A = A),
  control = list(adapt_delta = 0.999, max_treedepth=10)
  ,chains = 4, cores = 4, iter = 20000
)
## Compiling Stan program...
## Start sampling
## Warning: There were 6550 divergent transitions after warmup. See
## https://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup
## to find out why this is a problem and how to eliminate them.
## Warning: There were 6990 transitions after warmup that exceeded the maximum treedepth. Increase max_treedepth above 10. See
## https://mc-stan.org/misc/warnings.html#maximum-treedepth-exceeded
## Warning: There were 4 chains where the estimated Bayesian Fraction of Missing Information was low. See
## https://mc-stan.org/misc/warnings.html#bfmi-low
## Warning: Examine the pairs() plot to diagnose sampling problems
## Warning: The largest R-hat is 1.13, indicating chains have not mixed.
## Running the chains for more iterations may help. See
## https://mc-stan.org/misc/warnings.html#r-hat
## Warning: Bulk Effective Samples Size (ESS) is too low, indicating posterior means and medians may be unreliable.
## Running the chains for more iterations may help. See
## https://mc-stan.org/misc/warnings.html#bulk-ess
## Warning: Tail Effective Samples Size (ESS) is too low, indicating posterior variances and tail quantiles may be unreliable.
## Running the chains for more iterations may help. See
## https://mc-stan.org/misc/warnings.html#tail-ess
pairs(brm_centroid)

summary(brm_centroid)
## Warning: Parts of the model have not converged (some Rhats are > 1.05). Be
## careful when analysing the results! We recommend running more iterations and/or
## setting stronger priors.
## Warning: There were 6550 divergent transitions after warmup. Increasing
## adapt_delta above 0.999 may help. See
## http://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup
##  Family: skew_normal 
##   Links: mu = identity; sigma = identity; alpha = identity 
## Formula: T_centroid_lat ~ polymorphism + (1 | gr(species, cov = A)) 
##    Data: pi_subset (Number of observations: 59) 
##   Draws: 4 chains, each with iter = 20000; warmup = 10000; thin = 1;
##          total post-warmup draws = 40000
## 
## Group-Level Effects: 
## ~species (Number of levels: 59) 
##               Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept)     1.09      0.17     0.70     1.39 1.03      245     1290
## 
## Population-Level Effects: 
##                 Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept          -0.17      0.37    -0.85     0.61 1.03       89     2175
## polymorphismyes    -0.11      0.26    -0.61     0.28 1.11       23      160
## 
## Family Specific Parameters: 
##       Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma     0.20      0.20     0.01     0.69 1.10       37       56
## alpha    -1.58      3.94    -8.29     6.77 1.04       91     6601
## 
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).
## Check if the predicted values fits the rawdata
pp_check(brm_centroid)
## Using 10 posterior draws for ppc type 'dens_overlay' by default.

##Preliminary plots
plot(conditional_effects(brm_centroid))

They do not have differences in the latitude of the centroid

Evaluate if the colour monomorphic and colour polymorphic species differ in the body length

set.seed(30011994)
brm_bole <- brm(
  T_bole ~ polymorphism+(1| gr(species, cov = A)) ,
  data = pi_subset,
  family = gaussian(),
  #prior = prior,
  data2 = list(A = A),
  control = list(adapt_delta = 0.999, max_treedepth=10)
  ,chains = 4, cores = 4, iter = 20000
)
## Compiling Stan program...
## Start sampling
## Warning: There were 4435 divergent transitions after warmup. See
## https://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup
## to find out why this is a problem and how to eliminate them.
## Warning: There were 8599 transitions after warmup that exceeded the maximum treedepth. Increase max_treedepth above 10. See
## https://mc-stan.org/misc/warnings.html#maximum-treedepth-exceeded
## Warning: There were 4 chains where the estimated Bayesian Fraction of Missing Information was low. See
## https://mc-stan.org/misc/warnings.html#bfmi-low
## Warning: Examine the pairs() plot to diagnose sampling problems
## Warning: The largest R-hat is 1.11, indicating chains have not mixed.
## Running the chains for more iterations may help. See
## https://mc-stan.org/misc/warnings.html#r-hat
## Warning: Bulk Effective Samples Size (ESS) is too low, indicating posterior means and medians may be unreliable.
## Running the chains for more iterations may help. See
## https://mc-stan.org/misc/warnings.html#bulk-ess
## Warning: Tail Effective Samples Size (ESS) is too low, indicating posterior variances and tail quantiles may be unreliable.
## Running the chains for more iterations may help. See
## https://mc-stan.org/misc/warnings.html#tail-ess
pairs(brm_bole)

summary(brm_bole)
## Warning: Parts of the model have not converged (some Rhats are > 1.05). Be
## careful when analysing the results! We recommend running more iterations and/or
## setting stronger priors.
## Warning: There were 4435 divergent transitions after warmup. Increasing
## adapt_delta above 0.999 may help. See
## http://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup
##  Family: gaussian 
##   Links: mu = identity; sigma = identity 
## Formula: T_bole ~ polymorphism + (1 | gr(species, cov = A)) 
##    Data: pi_subset (Number of observations: 59) 
##   Draws: 4 chains, each with iter = 20000; warmup = 10000; thin = 1;
##          total post-warmup draws = 40000
## 
## Group-Level Effects: 
## ~species (Number of levels: 59) 
##               Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept)     1.03      0.13     0.77     1.25 1.08       32      487
## 
## Population-Level Effects: 
##                 Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept           0.05      0.32    -0.59     0.69 1.04     2179     3315
## polymorphismyes    -0.03      0.20    -0.41     0.38 1.03      156     3513
## 
## Family Specific Parameters: 
##       Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma     0.19      0.14     0.02     0.51 1.09       37       90
## 
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).
#r2
r2_bayes(brm_bole)
## # Bayesian R2 with Compatibility Interval
## 
##   Conditional R2: 0.971 (95% CI [0.809, 1.000])
##      Marginal R2: 0.005 (95% CI [1.525e-13, 0.035])
## Check if the predicted values fits the rawdata
pp_check(brm_bole)
## Using 10 posterior draws for ppc type 'dens_overlay' by default.

##Preliminary plots
plot(conditional_effects(brm_bole))

They do not have differences in body length

let’s Evaluate the association fo the predictors

lm_lat_range <- lm(T_lat_range ~ polymorphism+T_bole+T_centroid_lat, data=pi_subset)

check_collinearity(lm_lat_range)

The predictors are not collinear, we can use all of them in the models

6.2.2 Latitudinal range

set.seed(30011994)
brm_latrange_2 <- brm(
 T_lat_range ~ polymorphism+T_bole+T_centroid_lat + (1| gr(species, cov = A)) ,
  data = pi_subset,
  family = student(),
  #prior = prior,
  data2 = list(A = A),
  control = list(adapt_delta = 0.999, max_treedepth=10)
  ,chains = 4, cores = 4, iter = 20000
)
## Compiling Stan program...
## Start sampling
## Warning: There were 1 divergent transitions after warmup. See
## https://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup
## to find out why this is a problem and how to eliminate them.
## Warning: Examine the pairs() plot to diagnose sampling problems
pairs(brm_latrange_2)

summary(brm_latrange_2)
## Warning: There were 1 divergent transitions after warmup. Increasing
## adapt_delta above 0.999 may help. See
## http://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup
##  Family: student 
##   Links: mu = identity; sigma = identity; nu = identity 
## Formula: T_lat_range ~ polymorphism + T_bole + T_centroid_lat + (1 | gr(species, cov = A)) 
##    Data: pi_subset (Number of observations: 59) 
##   Draws: 4 chains, each with iter = 20000; warmup = 10000; thin = 1;
##          total post-warmup draws = 40000
## 
## Group-Level Effects: 
## ~species (Number of levels: 59) 
##               Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept)     0.44      0.32     0.02     1.13 1.00     1394     1541
## 
## Population-Level Effects: 
##                 Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept          -0.11      0.23    -0.58     0.34 1.00    15179     9107
## polymorphismyes     0.27      0.24    -0.21     0.75 1.00    22891    24974
## T_bole              0.14      0.14    -0.14     0.42 1.00    24891    25625
## T_centroid_lat     -0.47      0.16    -0.76    -0.14 1.00    11503    15156
## 
## Family Specific Parameters: 
##       Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma     0.69      0.16     0.31     0.95 1.00     1687     1435
## nu       20.13     13.90     2.87    55.25 1.00    26351    13427
## 
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).
#r2
r2_bayes(brm_latrange_2)
## # Bayesian R2 with Compatibility Interval
## 
##   Conditional R2: 0.426 (95% CI [0.155, 0.874])
##      Marginal R2: 0.345 (95% CI [0.143, 0.512])
## Check if the predicted values fits the rawdata
pp_check(brm_latrange_2)
## Using 10 posterior draws for ppc type 'dens_overlay' by default.

##Preliminary plots
plot(conditional_effects(brm_latrange_2))

6.2.3 Range size calculated with the area of the Convex polygon

area_polygon_2 <- brm(
 T_area_polygon ~ polymorphism+T_bole+T_centroid_lat + (1| gr(species, cov = A)),
  data = pi_subset,
  family = skew_normal(),
  #prior = prior,
  data2 = list(A = A),
  control = list(adapt_delta = 0.999, max_treedepth=10)
  ,chains = 4, cores = 4, iter = 20000
)
## Compiling Stan program...
## Start sampling
## Warning: There were 1 divergent transitions after warmup. See
## https://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup
## to find out why this is a problem and how to eliminate them.
## Warning: Examine the pairs() plot to diagnose sampling problems
pairs(area_polygon_2)

summary(area_polygon_2)
## Warning: There were 1 divergent transitions after warmup. Increasing
## adapt_delta above 0.999 may help. See
## http://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup
##  Family: skew_normal 
##   Links: mu = identity; sigma = identity; alpha = identity 
## Formula: T_area_polygon ~ polymorphism + T_bole + T_centroid_lat + (1 | gr(species, cov = A)) 
##    Data: pi_subset (Number of observations: 59) 
##   Draws: 4 chains, each with iter = 20000; warmup = 10000; thin = 1;
##          total post-warmup draws = 40000
## 
## Group-Level Effects: 
## ~species (Number of levels: 59) 
##               Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept)     0.43      0.26     0.02     1.01 1.00     3907     5467
## 
## Population-Level Effects: 
##                 Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept          -0.07      0.25    -0.60     0.38 1.00    19542    15643
## polymorphismyes     0.15      0.27    -0.37     0.69 1.00    21713    24500
## T_bole              0.18      0.15    -0.12     0.48 1.00    28270    27489
## T_centroid_lat      0.04      0.17    -0.30     0.38 1.00    23833    26439
## 
## Family Specific Parameters: 
##       Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma     0.89      0.14     0.61     1.16 1.00     5582     5341
## alpha     3.70      2.31    -0.67     8.90 1.00    17742    19912
## 
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).
#r2
r2_bayes(area_polygon_2)
## # Bayesian R2 with Compatibility Interval
## 
##   Conditional R2: 0.205 (95% CI [0.010, 0.540])
##      Marginal R2: 0.078 (95% CI [4.048e-04, 0.215])
## Check if the predicted values fits the rawdata
pp_check(area_polygon_2)
## Using 10 posterior draws for ppc type 'dens_overlay' by default.

##Preliminary plots
plot(conditional_effects(area_polygon_2))

6.2.4 Ecological regions

To indirectly explore the difference in niche width between colour monomorphic and polymorphic species, we measured the number of ecological regions occupy by each species using the geographical records and polygons. the ecological regions were obtained here

BRMS model exploring differences in the ecological regions occupy by monomorphic and polymorphic species based on geographical records

set.seed(30011994)
eco_reg_points_2 <- brm(
 eco_reg_points ~  polymorphism+T_bole+T_centroid_lat + (1| gr(species, cov = A)) ,
  data = pi_subset,
  family = poisson(),
  #prior = prior,
  data2 = list(A = A),
  control = list(adapt_delta = 0.999, max_treedepth=20)
  ,chains = 4, cores = 4, iter = 20000
)
## Compiling Stan program...
## Start sampling
pairs(eco_reg_points_2)

summary(eco_reg_points_2)
##  Family: poisson 
##   Links: mu = log 
## Formula: eco_reg_points ~ polymorphism + T_bole + T_centroid_lat + (1 | gr(species, cov = A)) 
##    Data: pi_subset (Number of observations: 59) 
##   Draws: 4 chains, each with iter = 20000; warmup = 10000; thin = 1;
##          total post-warmup draws = 40000
## 
## Group-Level Effects: 
## ~species (Number of levels: 59) 
##               Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept)     0.92      0.10     0.74     1.15 1.00     9305    16893
## 
## Population-Level Effects: 
##                 Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept           3.26      0.31     2.65     3.87 1.00     7750    14109
## polymorphismyes     0.31      0.19    -0.06     0.68 1.00     7719    14471
## T_bole              0.32      0.13     0.06     0.57 1.00     8831    14818
## T_centroid_lat     -0.01      0.12    -0.24     0.22 1.00     8440    14479
## 
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).
#r2
r2_bayes(eco_reg_points_2)
## # Bayesian R2 with Compatibility Interval
## 
##   Conditional R2: 0.966 (95% CI [0.946, 0.980])
##      Marginal R2: 0.166 (95% CI [0.005, 0.441])
## Check if the predicted values fits the rawdata
pp_check(eco_reg_points_2)
## Using 10 posterior draws for ppc type 'dens_overlay' by default.

##Preliminary plots
plot(conditional_effects(eco_reg_points_2))

BRMS model exploring differences in the ecological regions occupy by monomorphic and polymorphic species based on polygon

eco_reg_polygon_2 <- brm(
 eco_reg_polygon~ polymorphism+T_bole+T_centroid_lat + (1| gr(species, cov = A)) ,
  data = pi_subset,
  family = poisson(),
  #prior = prior,
  data2 = list(A = A),
  control = list(adapt_delta = 0.999, max_treedepth=20)
  ,chains = 4, cores = 4, iter = 20000
)
## Compiling Stan program...
## Start sampling
pairs(eco_reg_polygon_2)

summary(eco_reg_polygon_2)
##  Family: poisson 
##   Links: mu = log 
## Formula: eco_reg_polygon ~ polymorphism + T_bole + T_centroid_lat + (1 | gr(species, cov = A)) 
##    Data: pi_subset (Number of observations: 59) 
##   Draws: 4 chains, each with iter = 20000; warmup = 10000; thin = 1;
##          total post-warmup draws = 40000
## 
## Group-Level Effects: 
## ~species (Number of levels: 59) 
##               Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept)     1.04      0.11     0.84     1.29 1.00     6499    12865
## 
## Population-Level Effects: 
##                 Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept           3.82      0.35     3.12     4.51 1.00     6261    11414
## polymorphismyes     0.32      0.21    -0.08     0.72 1.00     6856    11511
## T_bole              0.25      0.14    -0.03     0.54 1.00     7193    12813
## T_centroid_lat     -0.10      0.13    -0.35     0.15 1.00     6916    11777
## 
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).
#r2
r2_bayes(eco_reg_polygon_2)
## # Bayesian R2 with Compatibility Interval
## 
##   Conditional R2: 0.981 (95% CI [0.971, 0.989])
##      Marginal R2: 0.148 (95% CI [0.001, 0.440])
## Check if the predicted values fits the rawdata
pp_check(eco_reg_polygon_2)
## Using 10 posterior draws for ppc type 'dens_overlay' by default.

##Preliminary plots
plot(conditional_effects(eco_reg_polygon_2))

6.2.5 Climatic zones

Addtionally, we also explored if colour monomorphic and polymorphic species differ in the number of climatic zones they occupy. We measured the number of climatic zones for each species using the geographical records and polygons. the Köppen-Geiger climate classification zones were obtained here

temp_zones_points_2 <- brm(
 temp_zones_points~ polymorphism+T_bole+T_centroid_lat + (1| gr(species, cov = A)) ,
  data = pi_subset,
  family = negbinomial(),
  #prior = prior,
  data2 = list(A = A),
  control = list(adapt_delta = 0.999, max_treedepth=20)
  ,chains = 4, cores = 4, iter = 20000
)
## Compiling Stan program...
## Start sampling
pairs(temp_zones_points_2)

summary(temp_zones_points_2)
##  Family: negbinomial 
##   Links: mu = log; shape = identity 
## Formula: temp_zones_points ~ polymorphism + T_bole + T_centroid_lat + (1 | gr(species, cov = A)) 
##    Data: pi_subset (Number of observations: 59) 
##   Draws: 4 chains, each with iter = 20000; warmup = 10000; thin = 1;
##          total post-warmup draws = 40000
## 
## Group-Level Effects: 
## ~species (Number of levels: 59) 
##               Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept)     0.08      0.06     0.00     0.21 1.00    18150    20046
## 
## Population-Level Effects: 
##                 Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept           2.19      0.07     2.04     2.32 1.00    50492    29794
## polymorphismyes     0.09      0.10    -0.10     0.28 1.00    68882    30031
## T_bole              0.19      0.05     0.08     0.30 1.00    56006    32956
## T_centroid_lat      0.06      0.05    -0.04     0.17 1.00    60393    31710
## 
## Family Specific Parameters: 
##       Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## shape   111.12     79.86    25.05   326.52 1.00    72428    30306
## 
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).
#r2
r2_bayes(temp_zones_points_2)
## # Bayesian R2 with Compatibility Interval
## 
##   Conditional R2: 0.369 (95% CI [0.167, 0.549])
##      Marginal R2: 0.329 (95% CI [0.119, 0.507])
## Check if the predicted values fits the rawdata
pp_check(temp_zones_points_2)
## Using 10 posterior draws for ppc type 'dens_overlay' by default.

##Preliminary plots
plot(conditional_effects(temp_zones_points_2))

temp_zones_polygon_2 <- brm(
 temp_zones_polygon~polymorphism+T_bole+T_centroid_lat+ (1| gr(species, cov = A)) ,
  data = pi_subset,
  family = negbinomial(),
  #prior = prior,
  data2 = list(A = A),
  control = list(adapt_delta = 0.999, max_treedepth=20)
  ,chains = 4, cores = 4, iter = 20000
)
## Compiling Stan program...
## Start sampling
pairs(temp_zones_polygon_2)

summary(temp_zones_polygon_2)
##  Family: negbinomial 
##   Links: mu = log; shape = identity 
## Formula: temp_zones_polygon ~ polymorphism + T_bole + T_centroid_lat + (1 | gr(species, cov = A)) 
##    Data: pi_subset (Number of observations: 59) 
##   Draws: 4 chains, each with iter = 20000; warmup = 10000; thin = 1;
##          total post-warmup draws = 40000
## 
## Group-Level Effects: 
## ~species (Number of levels: 59) 
##               Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept)     0.12      0.09     0.00     0.33 1.00    12553    16198
## 
## Population-Level Effects: 
##                 Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept           2.59      0.09     2.40     2.76 1.00    42286    26261
## polymorphismyes    -0.07      0.12    -0.31     0.17 1.00    66712    31409
## T_bole              0.01      0.07    -0.13     0.14 1.00    47442    31032
## T_centroid_lat     -0.24      0.07    -0.38    -0.11 1.00    61767    31816
## 
## Family Specific Parameters: 
##       Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## shape    11.35      8.47     4.79    27.69 1.00    27750    17123
## 
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).
#r2
r2_bayes(temp_zones_polygon_2)
## # Bayesian R2 with Compatibility Interval
## 
##   Conditional R2: 0.383 (95% CI [0.170, 0.552])
##      Marginal R2: 0.322 (95% CI [0.116, 0.504])
## Check if the predicted values fits the rawdata
pp_check(temp_zones_polygon_2)
## Using 10 posterior draws for ppc type 'dens_overlay' by default.

##Preliminary plots
plot(conditional_effects(temp_zones_polygon_2))

all_models<-NULL

for(mod in c("brm_latrange_2","area_polygon_2","eco_reg_points_2","eco_reg_polygon_2","temp_zones_polygon_2","temp_zones_points_2")){
baye_mode = get(mod)
  bayes_results<-baye_mode %>% 
  spread_draws(b_polymorphismyes)
  bayes_results<-tibble(b_polymorphismyes=bayes_results$b_polymorphismyes,model=mod)
  all_models<-bind_rows(all_models, bayes_results)
} 

all_models %>% ggplot(aes(y = model, x = b_polymorphismyes)) +
  stat_halfeye()+
  theme_classic()+
  geom_vline(xintercept = 0, linetype = "dashed",col="black",size=1)+
  labs(x="Estimate",y="Models")

Plot of the model

paleta1<-c("#1ABEC6","#FF5B00")

dataset_plot<-pi_subset %>% drop_na(T_lat_range|polymorphism|T_bole|T_centroid_lat)

dataset_plot$predict<-predict(brm_latrange_2,type="response")[,"Estimate"]

dataset_plot %>% ggplot(aes(x=polymorphism,y=predict,fill=polymorphism))+geom_point(aes(x=polymorphism,y=T_lat_range),shape = 21,size=3, position = position_jitterdodge(),alpha=0.5)+geom_violin(aes(x=polymorphism,y=T_lat_range),alpha=0.1, position = position_dodge(width = .75),size=1)+
  stat_summary(fun = mean,aes(color = polymorphism,group=polymorphism),fun.min = function(x) mean(x) - (2*se(x)),fun.max = function(x) mean(x)+(2*se(x)),geom = "pointrange",shape=22,size=1.5,col="black")+scale_fill_manual(values=paleta1)+scale_colour_manual(values=paleta1)+theme_classic()+labs(x="Colour polymorphism",y="Latitudinal range")

7 models without considering the phylogeny

We observed that the models with continous variables have values close to 0 and that the climatic zones models have random effects low variaces close to 0. This means that the phylogentic relationships of the individuals are not having a major effect on these models.

hyp <- "sd_species__Intercept^2 / (sd_species__Intercept^2 + sigma^2) = 0"
lat_range_sig <- hypothesis(brm_latrange_1, hyp, class = NULL)
area_sig<-hypothesis(area_polygon_1, hyp, class = NULL)

ggplot() + geom_histogram(aes(x = lat_range_sig$samples$H1, fill="Latitudinal range model"), alpha = 0.5)+
  geom_histogram(aes(x = area_sig$samples$H1,fill="Area polygon model"), alpha = 0.5)+labs(x="Pagel's lambda",y="Count")+theme_classic()
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

In consequence, we decided to run a set of models without considering the phylogeny. This let us include more species with good geographic records but that were not include in the phylogenetic reconstruction due to lack of genetic data.

7.1 Reload data

join_dataset<-read_csv("data_total.csv",col_names=T)
join_dataset$species<-gsub(pattern=" ", replacement="_",join_dataset$species)
#keep unique rows
join_dataset<-distinct(join_dataset,species,.keep_all = TRUE)
###Tranform island as binary
join_dataset<-join_dataset %>% mutate(bin_island=ifelse(cat_island=="island"|cat_island=="island_continent",1,0))
#Let's modify the dataset to deal with polytipic
join_dataset$polymorphism[which(join_dataset$polymorphism %in% c("polytipic","possible polytipic","pattern variable")==TRUE)]<-NA

7.2 Filter species with poor geographical information

Arachnids is one of the groups with the poorest geographic information available in public databases. For instance, in our data ~52% of the species has less than 50 geographical records

species_points<-join_dataset %>% drop_na(n_points)
species_geo<-nrow(species_points[species_points$n_points<50,])/nrow(species_points)*100
print(paste0(species_geo,"%"," of the species with geographical information has less than 50 geographical records"))
## [1] "52.0179372197309% of the species with geographical information has less than 50 geographical records"

To account for this, we decided to calculated the mean and its 95% confidence interval (CI) for the number of geographical records available for all the species. We excluded species from the subsequent analyses that fell outside the lower CI.

#Due to high vari
l_points<-na.omit(log(join_dataset$n_points))
##Let's calculate the 95% around the mean
library(boot)
data <- data.frame(xs = l_points)
bo <- boot(data[, "xs", drop = FALSE], statistic=meanfun, R=5000)
mean_ci<-boot.ci(bo, conf=0.95, type="bca")

ggplot(tibble(x=bo$t[,1]), aes(x=x)) +geom_density()+geom_segment(x=mean_ci$bca[4],xend=mean_ci$bca[5],y=0,yend=0,color="blue",size=2,lineend="round")

##Remove species with low number of records
datos_filtered<-join_dataset %>% filter(n_points>=exp(mean_ci$bca[4]))
#datos_filtered<-na.omit(datos_filtered)

##Let's save this dataset for further analyses

data_without_filtering<-datos_filtered

all the predictors seems skewed or not uniform distributed, let’s modify some predictors that may affect the regression due to their non-normal distribution

datos_filtered$T_centroid_lat<-abs(datos_filtered$centroid_lat)   
datos_filtered$T_lat_range<-sqrt(abs(datos_filtered$lat_range))
datos_filtered$T_area_polygon<-sqrt(datos_filtered$area_polygon+1)
datos_filtered$T_lat_range_wsc<-abs(datos_filtered$lat_range_wsc)
datos_filtered$T_area_countries_wsc<-sqrt(datos_filtered$area_countries_wsc)
datos_filtered$T_points<-log(datos_filtered$n_points)
datos_filtered$T_bole<-log(datos_filtered$bole_female)

Correlation plot between the variables

cor_matrix <- cor(na.omit(pi_subset[,c("T_points","T_centroid_lat","T_bole","T_lat_range","T_area_polygon","eco_reg_points","eco_reg_polygon","temp_zones_points","temp_zones_polygon")]))

colnames(cor_matrix)<c("T_points","T_centroid_lat","T_bole","T_lat_range","T_area_polygon","eco_reg_points","eco_reg_polygon","temp_zones_points","temp_zones_polygon")
## [1] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
rownames(cor_matrix)<-c("T_points","T_centroid_lat","T_bole","T_lat_range","T_area_polygon","eco_reg_points","eco_reg_polygon","temp_zones_points","temp_zones_polygon")
par(mfrow=c(1,1))
corrplot(cor_matrix, method = "number", type = "upper", order = "original", tl.cex=1, )

7.3 Analyses

Remove species from islands that can affect calculations due to their geographic limit for dispersion

datos_filtered_total<-datos_filtered %>% filter(cat_island != "island") %>% data.frame()

Standardize variable before the analysis, excluding the count variables

datos_filtered_total[,c("T_points","T_centroid_lat","T_bole","T_lat_range","T_area_polygon")]<-standard_varibles(datos_filtered_total[,c("T_points","T_centroid_lat","T_bole","T_lat_range","T_area_polygon")]) %>% data.frame()

Number of colour monomorphic and polymorphic species

table(datos_filtered_total$polymorphism)
## 
##  no yes 
##  53  41

Let’s run the models!

7.3.1 Association between colour polymorphism and the latitude of the centroid

Evaluate if the colour monomorphic and colour polymorphic species differ in the latitude of the centroid

set.seed(30011994)
brm_centroid <- brm(
  T_centroid_lat ~ polymorphism,
  data = datos_filtered_total,
  family = skew_normal(),
  #prior = prior,
  control = list(adapt_delta = 0.999, max_treedepth=10)
  ,chains = 4, cores = 4, iter = 20000
)
## Warning: Rows containing NAs were excluded from the model.
## Compiling Stan program...
## Start sampling
pairs(brm_centroid)

summary(brm_centroid)
##  Family: skew_normal 
##   Links: mu = identity; sigma = identity; alpha = identity 
## Formula: T_centroid_lat ~ polymorphism 
##    Data: datos_filtered_total (Number of observations: 94) 
##   Draws: 4 chains, each with iter = 20000; warmup = 10000; thin = 1;
##          total post-warmup draws = 40000
## 
## Population-Level Effects: 
##                 Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept           0.24      0.14    -0.03     0.51 1.00    25268    23684
## polymorphismyes    -0.49      0.21    -0.90    -0.08 1.00    25413    23777
## 
## Family Specific Parameters: 
##       Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma     1.01      0.08     0.87     1.19 1.00    22542    22290
## alpha    -0.69      1.86    -4.70     2.71 1.00    17557    18508
## 
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).
#r2
r2_bayes(brm_centroid)
## # Bayesian R2 with Compatibility Interval
## 
##   Conditional R2: 0.058 (95% CI [2.813e-09, 0.149])
## Check if the predicted values fits the rawdata
pp_check(brm_centroid)
## Using 10 posterior draws for ppc type 'dens_overlay' by default.

##Preliminary plots
plot(conditional_effects(brm_centroid))

They do not have differences in the latitude of the centroid

Evaluate if the colour monomorphic and colour polymorphic species differ in the body length

set.seed(30011994)
brm_bole <- brm(
  T_bole ~ polymorphism,
  data = datos_filtered_total,
  family = gaussian(),
  #prior = prior,
  control = list(adapt_delta = 0.999, max_treedepth=10)
  ,chains = 4, cores = 4, iter = 20000
)
## Warning: Rows containing NAs were excluded from the model.
## Compiling Stan program...
## Start sampling
pairs(brm_bole)

summary(brm_bole)
##  Family: gaussian 
##   Links: mu = identity; sigma = identity 
## Formula: T_bole ~ polymorphism 
##    Data: datos_filtered_total (Number of observations: 93) 
##   Draws: 4 chains, each with iter = 20000; warmup = 10000; thin = 1;
##          total post-warmup draws = 40000
## 
## Population-Level Effects: 
##                 Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept          -0.15      0.13    -0.41     0.12 1.00    29936    24931
## polymorphismyes     0.29      0.20    -0.11     0.69 1.00    30839    24686
## 
## Family Specific Parameters: 
##       Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma     0.98      0.07     0.85     1.14 1.00    30142    25118
## 
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).
#r2
r2_bayes(brm_bole)
## # Bayesian R2 with Compatibility Interval
## 
##   Conditional R2: 0.022 (95% CI [1.736e-10, 0.091])
## Check if the predicted values fits the rawdata
pp_check(brm_bole)
## Using 10 posterior draws for ppc type 'dens_overlay' by default.

##Preliminary plots
plot(conditional_effects(brm_bole))

They do not have differences in their body length

let’s Evaluate the association fo the predictors

lm_lat_range <- lm(T_lat_range ~ polymorphism+T_bole+T_centroid_lat, data=datos_filtered_total)

check_collinearity(lm_lat_range)

The predictors are not collinear, we can use all of them in the models

7.3.2 Latitudinal range

set.seed(30011994)
brm_latrange_3 <- brm(
 T_lat_range ~ polymorphism+T_bole+T_centroid_lat,
  data = datos_filtered_total,
  family = gaussian(),
  control = list(adapt_delta = 0.999, max_treedepth=10)
  ,chains = 4, cores = 4, iter = 20000
)
## Warning: Rows containing NAs were excluded from the model.
## Compiling Stan program...
## Start sampling
pairs(brm_latrange_3)

summary(brm_latrange_3)
##  Family: gaussian 
##   Links: mu = identity; sigma = identity 
## Formula: T_lat_range ~ polymorphism + T_bole + T_centroid_lat 
##    Data: datos_filtered_total (Number of observations: 93) 
##   Draws: 4 chains, each with iter = 20000; warmup = 10000; thin = 1;
##          total post-warmup draws = 40000
## 
## Population-Level Effects: 
##                 Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept          -0.13      0.12    -0.37     0.12 1.00    31251    26998
## polymorphismyes     0.21      0.19    -0.16     0.58 1.00    30427    26572
## T_bole              0.16      0.10    -0.04     0.36 1.00    27478    27499
## T_centroid_lat     -0.29      0.10    -0.49    -0.09 1.00    27541    26634
## 
## Family Specific Parameters: 
##       Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma     0.87      0.07     0.75     1.01 1.00    31497    26771
## 
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).
#r2
r2_bayes(brm_latrange_3)
## # Bayesian R2 with Compatibility Interval
## 
##   Conditional R2: 0.212 (95% CI [0.088, 0.332])
## Check if the predicted values fits the rawdata
pp_check(brm_latrange_3)
## Using 10 posterior draws for ppc type 'dens_overlay' by default.

##Preliminary plots
plot(conditional_effects(brm_latrange_3))

7.3.3 Range size calculated with the area of the Convex polygon

area_polygon_3 <- brm(
 T_area_polygon ~ polymorphism+T_bole+T_centroid_lat,
  data =datos_filtered_total,
  family = skew_normal(),
  control = list(adapt_delta = 0.999, max_treedepth=10)
  ,chains = 4, cores = 4, iter = 20000
)
## Warning: Rows containing NAs were excluded from the model.
## Compiling Stan program...
## Start sampling
pairs(area_polygon_3)

summary(area_polygon_3)
##  Family: skew_normal 
##   Links: mu = identity; sigma = identity; alpha = identity 
## Formula: T_area_polygon ~ polymorphism + T_bole + T_centroid_lat 
##    Data: datos_filtered_total (Number of observations: 92) 
##   Draws: 4 chains, each with iter = 20000; warmup = 10000; thin = 1;
##          total post-warmup draws = 40000
## 
## Population-Level Effects: 
##                 Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept          -0.06      0.13    -0.32     0.21 1.00    25150    26964
## polymorphismyes     0.16      0.19    -0.21     0.54 1.00    26544    25911
## T_bole              0.14      0.10    -0.06     0.34 1.00    25642    24010
## T_centroid_lat      0.10      0.11    -0.11     0.32 1.00    23371    25990
## 
## Family Specific Parameters: 
##       Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma     0.97      0.08     0.83     1.15 1.00    22407    24677
## alpha     3.44      1.27     1.51     6.46 1.00    21139    15885
## 
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).
#r2
r2_bayes(area_polygon_3)
## # Bayesian R2 with Compatibility Interval
## 
##   Conditional R2: 0.041 (95% CI [5.077e-04, 0.115])
## Check if the predicted values fits the rawdata
pp_check(area_polygon_3)
## Using 10 posterior draws for ppc type 'dens_overlay' by default.

##Preliminary plots
plot(conditional_effects(area_polygon_3))

7.3.4 Climatic zones

Addtionally, we also explored if colour monomorphic and polymorphic species differ in the number of climatic zones they occupy. We measured the number of climatic zones for each species using the geographical records and polygons. the Köppen-Geiger climate classification zones were obtained here

temp_zones_points_3 <- brm(
 temp_zones_points~ polymorphism+T_bole+T_centroid_lat ,
  data = datos_filtered_total,
  family = negbinomial(),
  #prior = prior,
  control = list(adapt_delta = 0.999, max_treedepth=20)
  ,chains = 4, cores = 4, iter = 10000
)
## Warning: Rows containing NAs were excluded from the model.
## Compiling Stan program...
## Start sampling
pairs(temp_zones_points_3)

summary(temp_zones_points_3)
##  Family: negbinomial 
##   Links: mu = log; shape = identity 
## Formula: temp_zones_points ~ polymorphism + T_bole + T_centroid_lat 
##    Data: datos_filtered_total (Number of observations: 93) 
##   Draws: 4 chains, each with iter = 10000; warmup = 5000; thin = 1;
##          total post-warmup draws = 20000
## 
## Population-Level Effects: 
##                 Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept           2.06      0.06     1.95     2.17 1.00    16109    13283
## polymorphismyes     0.11      0.08    -0.06     0.27 1.00    17547    14388
## T_bole              0.19      0.04     0.10     0.28 1.00    15352    14351
## T_centroid_lat      0.10      0.04     0.01     0.19 1.00    15517    13291
## 
## Family Specific Parameters: 
##       Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## shape    42.56     40.00    11.09   154.44 1.00    13946     9995
## 
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).
#r2
r2_bayes(temp_zones_points_3)
## # Bayesian R2 with Compatibility Interval
## 
##   Conditional R2: 0.201 (95% CI [0.073, 0.332])
## Check if the predicted values fits the rawdata
pp_check(temp_zones_points_3)
## Using 10 posterior draws for ppc type 'dens_overlay' by default.

##Preliminary plots
#plot(conditional_effects(temp_zones_points))
temp_zones_polygon_3 <- brm(
 temp_zones_polygon~polymorphism+T_bole+T_centroid_lat ,
  data = datos_filtered_total,
  family = negbinomial(),
  #prior = prior,
  control = list(adapt_delta = 0.999, max_treedepth=20)
  ,chains = 4, cores = 4, iter = 10000
)
## Warning: Rows containing NAs were excluded from the model.
## Compiling Stan program...
## Start sampling
pairs(temp_zones_polygon_3)

summary(temp_zones_polygon_3)
##  Family: negbinomial 
##   Links: mu = log; shape = identity 
## Formula: temp_zones_polygon ~ polymorphism + T_bole + T_centroid_lat 
##    Data: datos_filtered_total (Number of observations: 92) 
##   Draws: 4 chains, each with iter = 10000; warmup = 5000; thin = 1;
##          total post-warmup draws = 20000
## 
## Population-Level Effects: 
##                 Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept           2.59      0.07     2.46     2.72 1.00    15090    13188
## polymorphismyes    -0.04      0.10    -0.24     0.16 1.00    15822    13734
## T_bole              0.05      0.05    -0.05     0.16 1.00    14527    13067
## T_centroid_lat     -0.17      0.05    -0.28    -0.06 1.00    13719    12101
## 
## Family Specific Parameters: 
##       Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## shape     8.22      2.35     4.76    13.92 1.00    14735    11042
## 
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).
#r2
r2_bayes(temp_zones_polygon_3)
## # Bayesian R2 with Compatibility Interval
## 
##   Conditional R2: 0.196 (95% CI [0.058, 0.328])
## Check if the predicted values fits the rawdata
pp_check(temp_zones_polygon_3)
## Using 10 posterior draws for ppc type 'dens_overlay' by default.

##Preliminary plots
#plot(conditional_effects(temp_zones_polygon))

7.3.5 Summary of the models

all_models<-NULL

for(mod in c("brm_latrange_3","area_polygon_3","temp_zones_polygon_3","temp_zones_points_3")){
baye_mode = get(mod)
  bayes_results<-baye_mode %>% 
  spread_draws(b_polymorphismyes)
  bayes_results<-tibble(b_polymorphismyes=bayes_results$b_polymorphismyes,model=mod)
  all_models<-bind_rows(all_models, bayes_results)
} 

all_models %>% ggplot(aes(y = model, x = b_polymorphismyes)) +
  stat_halfeye()+
  theme_classic()+
  geom_vline(xintercept = 0, linetype = "dashed",col="black",size=1)+
  labs(x="Estimate",y="Models")

8 Island models

Considering that the presence on islands can be an indicator of range expansion, we also recorded whether species were distributed on islands by overlapping both sources of geographical distribution (occurrences and WSC) with the global shoreline vector from the islands database (Sayre et al., 2019).

We decided to test the association between colour polymorphism and the presence on islands using two datasets. The first one was using the species occurrences after discarding those species with poor geographic records as done here

##Remove species with low number of records
data_filtered_phylogeny<-data_filtered_phylogeny %>% drop_na(polymorphism) %>% drop_na(bin_island)
table(data_filtered_phylogeny$polymorphism)
## 
##  no yes 
##  56  35

This dataset includes 56 colour monomorphic species and 35 colour polymorphic species.


To increase the number of species in our analysis, we created a second dataset without filtering species based on the number of geographic records. We determined the presence on islands using the geographic distribution information available on the World Spider Catalog.

dataset_all_species_phylogeny<-dataset_all_species_phylogeny %>% drop_na(n_points) %>%drop_na(polymorphism) %>% drop_na(bin_island) %>% drop_na(cat_island_points)

table(dataset_all_species_phylogeny$polymorphism)
## 
##  no yes 
## 125  61

This second dataset includes 125 colour monomorphic species and 61 colour polymorphic species.

8.1 Presence on island using filtered dataset

##  Family: bernoulli 
##   Links: mu = logit 
## Formula: bin_island ~ 1 + polymorphism + log(bole_female) + (1 | gr(species, cov = A)) 
##    Data: data_filtered_phylogeny (Number of observations: 90) 
##   Draws: 4 chains, each with iter = 20000; warmup = 10000; thin = 1;
##          total post-warmup draws = 40000
## 
## Group-Level Effects: 
## ~species (Number of levels: 90) 
##               Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept)     3.86      4.01     0.29    13.01 1.00     4321     6240
## 
## Population-Level Effects: 
##                 Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept           3.33      4.18    -3.40    12.37 1.00    15262    10378
## polymorphismyes     4.73      3.38     1.14    13.14 1.00     8214     6157
## logbole_female     -0.13      1.60    -3.01     3.15 1.00    15035    10446
## 
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).
## # Bayesian R2 with Compatibility Interval
## 
##   Conditional R2: 0.463 (95% CI [0.069, 0.853])
##      Marginal R2: 0.023 (95% CI [1.740e-30, 0.247])

With this dataset there seems to be an association between colour polymorphism and the presence on islands

## .
##         0         1 
## 0.2142857 0.7857143
## .
##          0          1 
## 0.02857143 0.97142857

8.2 Presence on island using most of the species in phylogeny

tree=check_and_fix_ultrametric(join_tree)

missing<-tree$tip.label[which(tree$tip.label %in% dataset_all_species_phylogeny$species==FALSE)]

island_dataset_tree<-drop.tip(tree,missing)

island_dataset_tree$edge.length <- island_dataset_tree$edge.length / (max(island_dataset_tree$edge.length))

A <- ape::vcv(island_dataset_tree,corr = TRUE)

set.seed(30011994)

brm_island_2 <- brm(
  bin_island ~ 1 + polymorphism + log(bole_female) + (1| gr(species, cov = A)) ,
  data = dataset_all_species_phylogeny,
  family = bernoulli(),
  #prior = prior,
  data2 = list(A = A),
  control = list(adapt_delta = 0.999, max_treedepth=10)
  ,chains = 4, cores = 4, iter = 20000
)
## Warning: Rows containing NAs were excluded from the model.
## Compiling Stan program...
## Start sampling
## Warning: There were 10000 transitions after warmup that exceeded the maximum treedepth. Increase max_treedepth above 10. See
## https://mc-stan.org/misc/warnings.html#maximum-treedepth-exceeded
## Warning: Examine the pairs() plot to diagnose sampling problems
pairs(brm_island_2)

summary(brm_island_2)
##  Family: bernoulli 
##   Links: mu = logit 
## Formula: bin_island ~ 1 + polymorphism + log(bole_female) + (1 | gr(species, cov = A)) 
##    Data: dataset_all_species_phylogeny (Number of observations: 113) 
##   Draws: 4 chains, each with iter = 20000; warmup = 10000; thin = 1;
##          total post-warmup draws = 40000
## 
## Group-Level Effects: 
## ~species (Number of levels: 113) 
##               Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept)     5.93     10.86     0.86    20.84 1.00     1888     2723
## 
## Population-Level Effects: 
##                 Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept          -2.91     13.12   -19.80     4.68 1.00     4466     2961
## polymorphismyes     5.29      7.74     1.26    16.36 1.00     3418     3049
## logbole_female      2.72      5.09    -0.20    10.18 1.00     3430     3278
## 
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).
#r2
r2_bayes(brm_island_2)
## # Bayesian R2 with Compatibility Interval
## 
##   Conditional R2: 0.579 (95% CI [0.209, 0.949])
##      Marginal R2: 0.065 (95% CI [1.276e-24, 0.398])
## Check if the predicted values fits the rawdata
pp_check(brm_island_2)
## Using 10 posterior draws for ppc type 'dens_overlay' by default.

##Preliminary plots
#plot(conditional_effects(

With this dataset there seems to be an association between colour polymorphism and the presence on islands

## .
##     0     1 
## 0.472 0.528
## .
##         0         1 
## 0.1803279 0.8196721

A similar pattern is obtained when with run the model without the phylogeny

set.seed(30011994)

brm_island_3 <- brm(
  bin_island ~ 1 + polymorphism + log(bole_female),
  data = dataset_all_species_phylogeny,
  family = bernoulli(),
  #prior = prior,
  #data2 = list(A = A),
  control = list(adapt_delta = 0.999, max_treedepth=10)
  ,chains = 4, cores = 4, iter = 20000
)
## Warning: Rows containing NAs were excluded from the model.
## Compiling Stan program...
## Start sampling
pairs(brm_island_3)

summary(brm_island_3)
##  Family: bernoulli 
##   Links: mu = logit 
## Formula: bin_island ~ 1 + polymorphism + log(bole_female) 
##    Data: dataset_all_species_phylogeny (Number of observations: 113) 
##   Draws: 4 chains, each with iter = 20000; warmup = 10000; thin = 1;
##          total post-warmup draws = 40000
## 
## Population-Level Effects: 
##                 Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept          -0.03      0.87    -1.73     1.68 1.00    21025    22160
## polymorphismyes     2.21      0.84     0.77     4.06 1.00    14330    14208
## logbole_female      0.48      0.42    -0.33     1.32 1.00    19339    20752
## 
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).
#r2
r2_bayes(brm_island_3)
## # Bayesian R2 with Compatibility Interval
## 
##   Conditional R2: 0.105 (95% CI [0.024, 0.194])
## Check if the predicted values fits the rawdata
pp_check(brm_island_3)
## Using 10 posterior draws for ppc type 'dens_overlay' by default.

9 Conclusion

Lets observe how polymorphic and monomorphic species differ according to all the predictor. To build this graph we will use the linear models with the total data set and the Island model with the highest number of species.

all_models<-NULL

for(mod in c("brm_latrange_1","area_polygon_1","eco_reg_points_1","eco_reg_polygon_1","temp_zones_polygon_1","temp_zones_points_1","brm_island_2")){
baye_mode = get(mod)
  bayes_results<-baye_mode %>% 
  spread_draws(b_polymorphismyes)
  bayes_results<-tibble(b_polymorphismyes=bayes_results$b_polymorphismyes,model=mod)
  all_models<-bind_rows(all_models, bayes_results)
} 

all_models$model<-factor(all_models$model,levels=c("brm_island_2","temp_zones_polygon_1","temp_zones_points_1","eco_reg_polygon_1","eco_reg_points_1","area_polygon_1","brm_latrange_1"))

na.omit(all_models) %>% ggplot(aes(y = model, x = b_polymorphismyes, fill = after_stat(x < 0))) +
  stat_halfeye()+
  theme_classic()+
  geom_vline(xintercept = 0, linetype = "dashed",col="black",size=0.8)+
  labs(x="Estimate",y="Models")+
  xlim(-0.5,5)+
  scale_fill_manual(values = c("#BCCAEF","#D66D79" ))
## Warning: Removed 13295 rows containing missing values (`stat_slabinterval()`).

From all the variables and data filtering explored, we can conclude that monomorphic and polymorphic spider species in our dataset only differ in their presence on islands